59 ideas
23000 | Vicious regresses force you to another level; non-vicious imply another level [Baron/Miller] |
17824 | The master science is physical objects divided into sets [Maddy] |
8729 | Intuitionists deny excluded middle, because it is committed to transcendent truth or objects [Shapiro] |
23024 | A traveller takes a copy of a picture into the past, gives it the artist, who then creates the original! [Baron/Miller] |
8763 | The number 3 is presumably identical as a natural, an integer, a rational, a real, and complex [Shapiro] |
18249 | Cauchy gave a formal definition of a converging sequence. [Shapiro] |
8764 | Categories are the best foundation for mathematics [Shapiro] |
8762 | Two definitions of 3 in terms of sets disagree over whether 1 is a member of 3 [Shapiro] |
17825 | Set theory (unlike the Peano postulates) can explain why multiplication is commutative [Maddy] |
17826 | Standardly, numbers are said to be sets, which is neat ontology and epistemology [Maddy] |
17828 | Numbers are properties of sets, just as lengths are properties of physical objects [Maddy] |
17827 | Sets exist where their elements are, but numbers are more like universals [Maddy] |
17830 | Number theory doesn't 'reduce' to set theory, because sets have number properties [Maddy] |
8760 | Numbers do not exist independently; the essence of a number is its relations to other numbers [Shapiro] |
8761 | A 'system' is related objects; a 'pattern' or 'structure' abstracts the pure relations from them [Shapiro] |
17823 | If mathematical objects exist, how can we know them, and which objects are they? [Maddy] |
17829 | Number words are unusual as adjectives; we don't say 'is five', and numbers always come first [Maddy] |
8744 | Logicism seems to be a non-starter if (as is widely held) logic has no ontology of its own [Shapiro] |
8749 | Term Formalism says mathematics is just about symbols - but real numbers have no names [Shapiro] |
8750 | Game Formalism is just a matter of rules, like chess - but then why is it useful in science? [Shapiro] |
8752 | Deductivism says mathematics is logical consequences of uninterpreted axioms [Shapiro] |
8753 | Critics resent the way intuitionism cripples mathematics, but it allows new important distinctions [Shapiro] |
8731 | Conceptualist are just realists or idealist or nominalists, depending on their view of concepts [Shapiro] |
8730 | 'Impredicative' definitions refer to the thing being described [Shapiro] |
23008 | Grounding is intended as a relation that fits dependences between things [Baron/Miller] |
23018 | How does a changing object retain identity or have incompatible properties over time? [Baron/Miller] |
8725 | Rationalism tries to apply mathematical methodology to all of knowledge [Shapiro] |
23011 | Modern accounts of causation involve either processes or counterfactuals [Baron/Miller] |
23013 | The main process theory of causation says it is transference of mass, energy, momentum or charge [Baron/Miller] |
23014 | If causes are processes, what is causation by omission? (Distinguish legal from scientific causes?) [Baron/Miller] |
23015 | The counterfactual theory of causation handles the problem no matter what causes actually are [Baron/Miller] |
23016 | Counterfactual theories struggle with pre-emption by a causal back-up system [Baron/Miller] |
23009 | There is no second 'law' of thermodynamics; it just reflects probabilities of certain microstates [Baron/Miller] |
23002 | In relativity space and time depend on one's motion, but spacetime gives an invariant metric [Baron/Miller] |
22988 | The block universe theory says entities of all times exist, and time is the B-series [Baron/Miller] |
22991 | How can we know this is the present moment, if other times are real? [Baron/Miller] |
22992 | If we are actually in the past then we shouldn't experience time passing [Baron/Miller] |
22994 | Erzatz Presentism allows the existence of other times, with only the present 'actualised' [Baron/Miller] |
22998 | How do presentists explain relations between things existing at different times? [Baron/Miller] |
23017 | Presentism needs endurantism, because other theories imply most of the object doesn't exist [Baron/Miller] |
23023 | How can presentists move to the next future moment, if that doesn't exist? [Baron/Miller] |
22995 | Most of the sciences depend on the concept of time [Baron/Miller] |
22993 | For abstractionists past times might still exist, althought their objects don't [Baron/Miller] |
23001 | The error theory of time's passage says it is either a misdescription or a false inference [Baron/Miller] |
22999 | It is meaningless to measure the rate of time using time itself, and without a rate there is no flow [Baron/Miller] |
22986 | The C-series rejects A and B, and just sees times as order by betweenness, without direction [Baron/Miller] |
22996 | The A-series has to treat being past, present or future as properties [Baron/Miller] |
23007 | The B-series can have a direction, as long as it does not arise from temporal flow [Baron/Miller] |
23003 | Static theories cannot account for time's obvious asymmetry, so time must be dynamic [Baron/Miller] |
23004 | The direction of time is either primitive, or reducible to something else [Baron/Miller] |
23005 | The kaon does not seem to be time-reversal invariant, unlike the rest of nature [Baron/Miller] |
23006 | Maybe the past is just the direction of decreasing entropy [Baron/Miller] |
23010 | We could explain time's direction by causation: past is the direction of causes, future of effects [Baron/Miller] |
22989 | Static time theory presents change as one property at t1, and a different property at t2 [Baron/Miller] |
23020 | If a time traveller kills his youthful grandfather, he both exists and fails to exist [Baron/Miller] |
23022 | Presentism means there no existing past for a time traveller to visit [Baron/Miller] |
22987 | The past (unlike the future) is fixed, along with truths about it, by the existence of past objects [Baron/Miller] |
22990 | The moving spotlight says entities can have properties of being present, past or future [Baron/Miller] |
22997 | The present moment is a matter of existence, not of acquiring a property [Baron/Miller] |